Provide two different degrees of rotation less than 75 deg but greater than that will turn a regular dodecagon onto itself. A regular dodecagon will turn onto itself after a and rotation.

Answer 1

A regular dodecagon has 12 sides, and each angle of a regular dodecagon is 150 degrees.

To find the degrees of rotation that will turn a regular dodecagon onto itself, we need to find the numbers that are multiples of 360 degrees plus the original angle.

1. First, let's find the smallest multiple of 360 degrees that is greater than 150 degrees:
360 * 1 = 360 degrees
Since 360 degrees is too large, let's find the next multiple:
360 * 2 = 720 degrees

Now we can find the rotation angle:
Rotation angle = 720 degrees - 150 degrees = 570 degrees

Therefore, a rotation of 570 degrees will turn a regular dodecagon onto itself.

2. Let's find another smaller multiple of 360 degrees that is greater than 150 degrees:
360 * 3 = 1080 degrees

Now we can find the rotation angle:
Rotation angle = 1080 degrees - 150 degrees = 930 degrees

Therefore, a rotation of 930 degrees will also turn a regular dodecagon onto itself.